Robust observer design via factorization approach

Problems of designing robust observers in the frequency domain are formulated and solved. Using the factorization approach, a characterization of all observers is derived. This enables the description of all achievable transfer functions of estimate errors in terms of a RH_∞-parameter matrix. It is shown that the problem of designing optimally robust observers can therefore be transformed into the well-known model matching problem that can be solved with H_∞-optimization techniques. It is shown that the proposed methods can be used to solve the problem of finding exact unknown input observers